This document provides an outline for a course on Logic and Set Theory. The course aims to teach students about topics like propositions, logical operators, rules of inference, algebra of logic, quantifiers, elementary set theory concepts, and theorems on sets and set operations. The course objectives are for students to apply logical principles, construct truth tables, represent mathematical statements, and apply set theoretic concepts and thinking processes to solve problems. The course also provides intended learning outcomes at the program and course level, as well as a proposed teaching plan with topics, activities, and assessments across several weeks.

1. GOV. ALFONSO D. TAN COLLEGE
Bachelor of Secondary Education Major in Mathematics
Outcomes – Based Teaching and Learning Plan in ME 103
Course Title Logic and Set Theory Course Code ME103
Credit Units 3 units Course Pre-/Co-requisites None
Course Description
(CMO 75 s. 2017)
This course is a study of mathematical logic which covers topics such as, propositions, logical operators, rules of replacement, rules of inference, algebra of
logic and quantifiers. It also covers a discussion of elementary theory of sets such as fundamental concepts of sets and s et operations. Theorems on sets
and set operations will be proven using the rules of replacements and inferences in symbolic logic.
Institute Intended
Learning Outcomes
Graduates of BSEd will have the ability to:
a. Articulate the rootedness of education in philosophical, socio cultural, historical, psychological, and political concept
b. Demonstrate mastery of subject matter/discipline
c. Facilitate learning using a wide range of teaching methodologies and delivery modes appropriate to specific learners and their environments
d. Develop innovative curricula, instructional plans, teaching, approaches, and resources for diverse learners.
e. Apply skills in the development and utilization of ICT to promote, quality, relevant, and sustainable educational practices.
f. Demonstrate a variety of thinking skills in planning, monitoring, assessing, and reporting learning processes and outcomes
g. Practice professional and ethical teaching standards sensitive to the local, national, and global realities.
h. Pursue lifelong learning for professional growth through varied experiential and field-based opportunities.
Program Intended
Learning Outcomes
(PILO)
At the end of this program, students will be able to:
a. Exhibit competence in mathematical concepts and procedures.
b. Exhibit proficiency in relating mathematics to other curricular areas.
c. Manifest meaningful and comprehensive pedagogical content knowledge (PCK) of mathematics.
d. Demonstrate competence in designing, constructing and utilizing different forms of assessment in mathematics.
e. Demonstrate proficiency in problem-solving by solving and creating routine and non-routine problems with different levels of complexity.
f. Use effectively appropriate approaches, methods, and techniques in teaching mathematics including technological tools.
g. Appreciate mathematics as an opportunity for creative work, moments of enlightenment, discovery and gaining insights of the world.
Course Intended
Learning Outcomes
(CILO)
At the end of this course, the students should be able to:
a. Apply the principles of logic to tell sound from unsound reasoning in everybody discourse.
b. Construct truth tables for logical expressions; test statements for logical equivalence and represent mathematical statements in the language of
predicate language.
c. Apply the appropriate set theoretic concepts, thinking process, tools and techniques in the solution to various conceptual or real-world problem.
Alfonsos as Lux Mundi: Serving Humanity with Empowered Mind, Passionate Heart and Virtuous Soul

2. MIDTERM Essential Learning
Intended Learning
Outcome (ILO)
Suggested
Teaching/Learning
Activities (TLAs)
Assessment
Tasks (ATs)Week Content Standards Declarative Knowledge Functional Knowledge
1 – 4
Demonstrate knowledge
of The Logic of
Compound Statements
I. Logic and Compound
Statements
A. Logical Form and Logical
Equivalence
*Discussing Statements and
compound Statements
*Constructing Truth Tables
*Evaluating the Truth of More
General Compound Statements
*Discussing Logical Equivalence
*Comparing Tautologies and
Contradictions
*Identify compound
statements
*Construct truth tables for
compound statement
*Determine the truth value of
the statements
*Examine the statements
whether Logically equivalent
or not
*Compare Tautologies and
Contradictions
Lecture
Pair/Group Exercises
Interactive Discussion
Evaluative Test
Oral Recitation
B. Conditional Statements
*discussing Logical Equivalence
Involving (Implication)
*representing If-Then as Or
*determining the negation,
contrapositive, inverse and converse
of conditional statements
*Comparing Only-If and Biconditional
*Evaluating necessary and sufficient
conditions
*Construct truth tables to
show logical equivalence of
statements
*verify the logical
equivalence of statements
*determine the negative,
contrapositive, inverse and
converse of conditional
statements and state whether
logically equivalents
Problem exercises
Group/Class Discussion
Lecture
Paper and Pencil
Test
Evaluative Test
C. Valid and Invalid
Arguments
*discussing Valid Argument Forms,
rules of inference, fallacies and
contradictions
*determine the validity of the
argument
*use the rules of inference to
prove that arguments are
valid or invalid
*differentiate fallacies and
rules of inference in
determine the validity of
arguments
Lecture
Pair/Group Exercises
Interactive Discussion
Evaluative Test
Oral Recitation
5-9
Demonstrate knowledge
of Logic and Quantified
Statements
A. Predicates and Quantified
Statements
Discussing the Universal and
Existential quantifier
Differentiating Formal and informal
language
Differentiating Universal and
Existential Statements and their
equivalent forms
Discussing the negation of Quantified
and universal conditional statements
Define quantifiers
Show the difference of formal
and informal language by
giving examples
Compare the universal and
existential statements and
give the equivalent forms
Illustrate the process of
negating the quantified
statements and the universal
Lecture
Interactive Discussion
Seatwork
Quiz
Assignment

3. conditional statements
B. Statements with Multiple
Quantifiers
Translating from Informal to Formal
language;
Simplifying Ambiguous Language
Negating Multiply-Quantified
Statements
Discussing the Order of Quantifiers
Translate informal to formal
language
Simplify ambiguous language
Clarify the order of quantities
Lecture
Collaboration
Learning Station
Paper and pencil
Test
Assignment
Evaluative Test
C. Arguments with Quantified
Statements
Discussing the Universal Modus
Ponens and its use in a proof
Discussing the Universal Modus
Tollens
Proving the Validity of Arguments
with Quantified statements
Using Diagrams to Test for Validity
Creating Additional forms of
Arguments
Use Universal Modus
Ponens and universal Modus
Tollens in Proving the Validity
of Statements
Use diagrams to test for
Validity
Create Additional Forms of
Arguments
Lecture
Collaboration
Learning Station
Evaluative Test
Oral Recitation
FINAL
10-11
Demonstrate Knowledge
of Set Theory: Definitions
and the Element Method
of Proof
III. Set Theory
 Subsets
 Proof and Disproof
 Set Equality
 Venn Diagrams
 Operations on Sets
 The Empty Set
 Partitions of Sets
 Power Sets
 Cartesian Products
Discussing the subsets
Showing the process of proving and
disproving set properties
Using Venn Diagrams to show set
relations
Performing the operations of sets
Discussing the empty set
Discussing the partitions of sets
Determine whether a set is a
subset of a given set or not
Prove and disprove set
properties
Use Venn Diagrams to show
set relations
Perform Operations of sets
Identify whether a set is
empty or not
Identify whether sets are
partitions of a given set
Lecture
Interactive discussion
Skills Exercises
Collaboration
Problem Solving
Graphic Organizer
with Rubrics
Paper and Pencil
Test
12-13
Demonstrate Knowledge
of the Properties of Sets
Set Identities
How to prove Set Identifies
How to Prove an Empty Set
Discussing Set identities
Proving Set identities
Proving and Empty Set
Identify and explain set
identities
Prove set identities
Prove whether a set is empty
or nots
Lecture
Group Discussion
Problem Solving
Paper and pencil
test
Assignment

4. 14-15
Demonstrate Knowledge
of Disproofs and
Algebraic Proofs
Disproving an Alleged Set
Properties
Problem Solving Strategy
The Number of Subsets of a
Set
Algebraic Proofs of Set
Identities
Disproving Set properties
Using problem solving strategy
Determining the number of subsets
of a set
applying algebraic proofs of set
identities
Disprove set properties
Use problem solving strategy
Determine the number of
subsets of a set
Apply algebraic proofs of set
identities
Lecture
Group Discussion
Problem Solving
Evaluative Test
Oral Recitation
16-18 Demonstrate Knowledge
of Boolen Algebras and
Russell’s Para
Boolean Algebras
Description of Rusell’s
Paradox
Using Boolean Algebras to prove set
relations
Simplifying Russel’s Paradox
Use Boolean algebras to
prove set relations
Simplify Russel’s Paradoz
Lecure
Group discussion
Quiz
Group activity
Basic Readings
Epp, S. (2012). Discrete Mathematics. Cengage Learning Asia Pte Ltd. ISBN-13: 13-978-1-285-13049-1
Extended Readings http://www.dlsu.edu.ph/academics/colleges/cos/math/syllabus/intoset.pdf
Course Assessment As identifiedin the Assessment Task

5. Course Policies
LanguageofInstructions
English
Attendance
 As identifiedin the student handbook
Homework,Quizzes,Exams
Special Requirement
GradingSystem
Quiz - 30%
Performance - 40%
Exam -30%
Total 100%
Classroom RulesandRegulations
 As identified in the student handbook
Committee Members Committee Leader : NorielB. Erap, M.Ed.
Members : Elton JohnB. Embodo
Fritzie Azuelo
ClintJoy Quije
ZarleneM.Tigol
RogelouAndam
AlemarC. Mayordo
Consultation Schedule FacultyMember : EltonJohn B. Embodo
ContactNumber : 09107619989
E-mailaddress : eltonjohn439@yahoo.com
ConsultationHours: 3:00 PM – 6:00PM
TimeandVenue : 3:00 PM – 6:00PM Wednesday
Course Title A.Y. Term of Effectivity Prepared by Approved by Page/s
LOGIC AND SET THEORY 2018-2019 Elton John B. Embodo
Instructor
Love H. Falloran, MSCrim
VP for Academic Affairs
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